# What is the factors for x^3 + 3x^2 - x - 3?

May 2, 2015

${x}^{3} + 3 {x}^{2} - x - 3$

We can make groups of 2 terms like this:

$\left({x}^{3} + 3 {x}^{2}\right) - \left(x + 3\right)$

$= {x}^{2} \left(x + 3\right) - 1 \left(x + 3\right)$

$= \left(x + 3\right)$ is common to both the terms

$= \left(x + 3\right) \left({x}^{2} - 1\right)$

$= \left(x + 3\right) \left({x}^{2} - {1}^{2}\right)$

We know that color(blue)(a^2 - b^2 = (a+b)(a-b)

 = color(green)((x + 3)(x+1)(x - 1)

x+3 ; x+1; x-1 are the factors of ${x}^{3} + 3 {x}^{2} - x - 3$